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Volume 8, Issue 6
Two-Level Defect-Correction Method for Steady Navier-Stokes Problem with Friction Boundary Conditions

An Liu, Yuan Li & Rong An

DOI: 10.4208/aamm.2014.m595

Adv. Appl. Math. Mech., 8 (2016), pp. 932-952.

Published online: 2018-05

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  • Abstract

In this paper, we present two-level defect-correction finite element method for steady Navier-Stokes equations at high Reynolds number with the friction boundary conditions, which results in a variational inequality problem of the second kind. Based on Taylor-Hood element, we solve a variational inequality problem of Navier-Stokes type on the coarse mesh and solve a variational inequality problem of Navier-Stokes type corresponding to Newton linearization on the fine mesh. The error estimates for the velocity in the $H^1$ norm and the pressure in the $L^2$ norm are derived. Finally, the numerical results are provided to confirm our theoretical analysis.

  • Keywords

Navier-Stokes equations, friction boundary conditions, variational inequality problems, defect-correction method, two-level mesh method.

  • AMS Subject Headings

65N30, 76M10

  • Copyright

COPYRIGHT: © Global Science Press

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  • TXT
@Article{AAMM-8-932, author = {Liu , AnLi , Yuan and An , Rong}, title = {Two-Level Defect-Correction Method for Steady Navier-Stokes Problem with Friction Boundary Conditions}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2018}, volume = {8}, number = {6}, pages = {932--952}, abstract = {

In this paper, we present two-level defect-correction finite element method for steady Navier-Stokes equations at high Reynolds number with the friction boundary conditions, which results in a variational inequality problem of the second kind. Based on Taylor-Hood element, we solve a variational inequality problem of Navier-Stokes type on the coarse mesh and solve a variational inequality problem of Navier-Stokes type corresponding to Newton linearization on the fine mesh. The error estimates for the velocity in the $H^1$ norm and the pressure in the $L^2$ norm are derived. Finally, the numerical results are provided to confirm our theoretical analysis.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.2014.m595}, url = {http://global-sci.org/intro/article_detail/aamm/12124.html} }
TY - JOUR T1 - Two-Level Defect-Correction Method for Steady Navier-Stokes Problem with Friction Boundary Conditions AU - Liu , An AU - Li , Yuan AU - An , Rong JO - Advances in Applied Mathematics and Mechanics VL - 6 SP - 932 EP - 952 PY - 2018 DA - 2018/05 SN - 8 DO - http://doi.org/10.4208/aamm.2014.m595 UR - https://global-sci.org/intro/article_detail/aamm/12124.html KW - Navier-Stokes equations, friction boundary conditions, variational inequality problems, defect-correction method, two-level mesh method. AB -

In this paper, we present two-level defect-correction finite element method for steady Navier-Stokes equations at high Reynolds number with the friction boundary conditions, which results in a variational inequality problem of the second kind. Based on Taylor-Hood element, we solve a variational inequality problem of Navier-Stokes type on the coarse mesh and solve a variational inequality problem of Navier-Stokes type corresponding to Newton linearization on the fine mesh. The error estimates for the velocity in the $H^1$ norm and the pressure in the $L^2$ norm are derived. Finally, the numerical results are provided to confirm our theoretical analysis.

Liu , AnLi , Yuan and An , Rong. (2018). Two-Level Defect-Correction Method for Steady Navier-Stokes Problem with Friction Boundary Conditions. Advances in Applied Mathematics and Mechanics. 8 (6). 932-952. doi:10.4208/aamm.2014.m595
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